The present invention relates to a method for vulcanizing a tire by predetermining its degree (level) of vulcanization.
In the field of tire production, models of vulcanization kinetics have been developed in order to improve the vulcanization cycles. A history of the temperature of the vulcanization cycle is generally used in the attempt to improve the vulcanization according to the model. These models, however, have proved to be either complicated or of low reliability.
The object of the present invention is to avoid the problems and overcome the limitations of the known methods.
In one aspect, the invention relates to a method for vulcanizing a tire by predetermining the change of its state of vulcanization in time by means of a parameter consisting of its degree of vulcanization, the said tire comprising specified vulcanizable mixtures and specified fabrics, the said vulcanization being carried out by means of a vulcanization mould heated by heat-supply fluids and by subjecting the said tire to cooling by means of a specified cooling fluid, the said method comprising the steps of:
a) determining specified structural and dimensional parameters (geometry) of the said tire and the said mould,
b) determining the change over a time t of specified thermodynamic parameters, comprising the temperature T(t) and diffusivity xcex1 of the said tire, mould, heat-supply fluid and cooling fluid,
c) determining a parameter consisting of an equivalent vulcanization time t0 which, at a specified constant reference temperature T0, makes it possible to obtain an equivalent degree of vulcanization X(t0) equal to the degree of vulcanization X(t) obtained at a specified instant t and at a specified temperature T(t) variable in time, the said equivalent vulcanization time t0 being obtained by means of a specified function of the said reference temperature T0, of the said temperature T(t) and of the said time t,
d) determining the said equivalent degree of vulcanization X(t0) at specified points within the said tire when the said equivalent vulcanization time t0 varies, the said degree of vulcanization X(t0) being obtained by means of an equivalent isothermal rheometric curve, at the said reference temperature T0, comprising three consecutive sections having the following equations:       X    ⁡          (              t        o            )        =      {                                                      k              ⁢                              xe2x80x83                            ⁢                              t                o                n                                                    1              +                              k                ⁢                                  xe2x80x83                                ⁢                                  t                  o                  n                                                                                                                                                      k                  x                                ⁢                                  t                  o                                      n                    x                                                                              1                +                                                      k                    x                                    ⁢                                      t                    o                                          n                      x                                                                                            +                          f              ⁡                              (                                                      t                    o                                    -                                      t                    xx                                                  )                                                                                      1            -                          C              ⁢                                                                                          k                      R                                        ⁡                                          (                                                                        t                          o                                                -                                                  t                          100                                                                    )                                                                            n                    R                                                                    1                  +                                                                                    k                        R                                            ⁡                                              (                                                                              t                            o                                                    -                                                      t                            100                                                                          )                                                                                    n                      R                                                                                                              
xe2x80x83where the aforesaid first equation is valid for a t0 less than or equal to a first specified equivalent time value (t0xe2x89xa6t60) at which there is a first specified equivalent degree of vulcanization (X(t60)=60%), the aforesaid third equation is valid for a t0 greater than or equal to a second specified equivalent time value (t0xe2x89xa7t100) at which there is a second specified value of the equivalent degree of vulcanization (X(t100)=100% or 1), and the aforesaid second equation is valid for a t0 lying between the said first and second values of the said equivalent time (t60xe2x89xa6t0xe2x89xa6t100),
where txx is a third specified equivalent time value, intermediate between the said first (t60) and second (t100) equivalent time value, at which there is a third specified value of the equivalent degree of vulcanization (X(txx)=90%),
where f(t0xe2x88x92txx) is a cubic interpolation function which, for a t0 less than or equal to the said third equivalent time value (t0xe2x89xa6txx), is equal to 0, while, for a t0 lying between the said third equivalent time value and the said second equivalent time value (txxxe2x89xa6t0xe2x89xa6t100), it is such that the function X(t0) passes through an intermediate point consisting of the said intermediate value of the equivalent degree of vulcanization (X(txx)) and terminates with a horizontal tangent at a point consisting of the said second value of equivalent degree of vulcanization X(t100),
where C is equal to 1 xe2x88x92X∞, X∞ being a fourth, asymptotic value of the equivalent degree of vulcanization which is present for the equivalent time value tending towards infinity, and where each pair of the aforesaid parameters (n, k; nx, kx; nR, kR) is determined by setting a corresponding pair of values of equivalent degree of vulcanization (X1, X2), determining the corresponding equivalent vulcanization times (t1, t2) by the procedure described in point c), and obtaining from each of the aforesaid three equations a system of two equations with three unknowns.
Preferably, in said step b) the said temperature (T) is determined by means of the following steps:
b1) finite element modelling of the said tire and the said mould by means of a lattice (mesh) formed from specified finite elements and nodes;
b2) assigning initial contour conditions by the association of specified initial temperatures with each of the aforesaid nodes,
b3) determining the variation in time of the temperature and convection coefficient of the said fluids for supplying heat to the said mould during the said vulcanization,
b4) determining the variation in time of the temperature and convection coefficient of the said cooling fluid during the cooling of the said tire,
b5) determining the change in time of the said temperature T(t) at specified points within the said tire and the said mould, by means of the Fourier equation for heat transmission, solved by the finite element method.
Advantageously, the said specified function by means of which the said equivalent vulcanization time t0 is determined in step c) is expressed as follows:             t      0        ⁢          (      t      )        =            ∫      0      t        ⁢                  ⅇ                  α          ⁢                      xe2x80x83                    ⁢                                                    T                ⁢                                  (                  t                  )                                            -                              T                0                                                                    (                                                      T                    ⁢                                          (                      t                      )                                                        ·                                      T                    0                                                  )                            β                                          ⁢              ⅆ        t            
where T(t) is found in the preceding step b5), and xcex1 and xcex2 are determined by means of three isothermal rheometric diagrams obtained from test specimens of each mixture at three specified temperatures (TA, TB, TC), each rheometric diagram representing the change of the torque Sxe2x80x2 and of the corresponding degree of vulcanization (XA(t); XB(t); XC(t)) of the said mixture as a function of time, xcex2 being found by means of the aforesaid equation using the aforesaid three temperatures (TA, TB, TC) and three time increments (xcex94tA, xcex94tB, xcex94tC) which cause the degree of vulcanization to change from a first specified value X11 to a second specified value X21 in the aforesaid three rheometric diagrams, and xcex1 is found by means of the aforesaid equation using two of the aforesaid temperatures (TA, TB) and two of the said time increments (xcex94tA, xcex94tB) of two of the aforesaid three rheometric diagrams.
Preferably, the method also comprises the following step:
e) determining a parameter consisting of a torque Sxe2x80x2 at a specified temperature T, given the aforesaid degree of vulcanization X(t0), by means of the following function:
Sxe2x80x2(T, X)=Sxe2x80x2min(T)+X*(Sxe2x80x2max(T)xe2x88x92Sxe2x80x2min(T))
where   "AutoLeftMatch"      "AutoLeftMatch"          xe2x80x83        ⁢          "AutoLeftMatch"              {                                                                                                  S                    min                    xe2x80x2                                    ⁡                                      (                    T                    )                                                  =                                                                            S                      xe2x80x2                                        ⁡                                          (                                              T                        ,                        0                                            )                                                        =                                                                                    S                        min                        xe2x80x2                                            ⁡                                              (                                                  T                          0                                                )                                                              +                                                                  D                        min                                            ⁡                                              (                                                  T                          -                                                      T                            0                                                                          )                                                                                                                                                                                                          S                    max                    xe2x80x2                                    ⁡                                      (                    T                    )                                                  =                                                                            S                      xe2x80x2                                        ⁡                                          (                                              T                        ,                        1                                            )                                                        =                                                                                    S                        max                        xe2x80x2                                            ⁡                                              (                                                  T                          0                                                )                                                              +                                                                  D                        max                                            ⁡                                              (                                                  T                          -                                                      T                            0                                                                          )                                                                                                                                    
and where Sxe2x80x2min(T0)=minimum torque at the said reference temperature T0; Sxe2x80x2max(T0)=maximum torque at the said reference temperature T0; Dmin=derivative of Sxe2x80x2min with respect to the said temperature T; Dmax=derivative of Sxe2x80x2max with respect to the said temperature T.
Preferably, the aforesaid pair of values of the equivalent degree of vulcanization (X1, X2) consists of X1=30% and X2=60% for the aforesaid first equation.
In turn, the aforesaid pair of values of the equivalent degree of vulcanization (X1, X2) consists of X1=60% and X2=90% for the aforesaid second equation.
Preferably, the aforesaid pair of values of the equivalent degree of vulcanization (X1, X2) consists of X1=20% and X2=60% for the aforesaid third equation, the reduction of X for t tending towards infinity being set at XR=100%.
The method according to the invention is based essentially
on the determination of the temperature distribution within a tire as a function of time, by means of a finite element (FEA) modelling which simulates the change of the temperature at each point within the tire, given the history of the temperatures at the contour, and
on the determination of the distribution of the consequent state of vulcanization by means of a vulcanization model implemented within the finite element model; the vulcanization model consists of a procedure (routine), integrated in the FEA model, which, instant by instant, determines the state of vulcanization at each point of the tire, using a model of the degree of vulcanization (X) based on the rheometric behaviour of the mixtures.
The method according to the invention requires the following input data:
structure and geometry of the tire;
thermodynamic characteristics of the mixtures;
geometry and conductivity of the mould;
vulcanization timetable;
conditions of cooling of the tire.
Normally, the vulcanization timetable is drawn up in tabular form and shows the variation in time of the temperature of the fluids supplying heat to the components of the mould, namely the sectors, the cheeks, and any vulcanization chamber or inner metal mould. The fluids consist of steam for heating the sectors (tread), steam for heating the cheeks (sidewalls), steam for the first inflation of the vulcanization chamber and water or inert gas for the second inflation of the vulcanization chamber.
The method provides the following output data:
map of the temperature distribution;
map of the true and conventional degree of vulcanization and of parameters connected with it (for example, the equivalent time and the torque).
In the method according to the invention, the FEA model is also extended to the mould and to the vulcanization chamber. By assigning the values of the temperatures which appear on the vulcanization timetable, therefore, the model can supply the correct temperatures at the contour of the tire.
The evaluation of the state of vulcanization by means of the degree of vulcanization has the advantage of using a parameter which is independent of the mixture; the vulcanization process is completed when the degree of vulcanization is equal to 1.
However, the conventional criterion of evaluation of the state of vulcanization, based on the equivalent times, has the disadvantage of being dependent on the mixture.
The method according to the invention makes it possible to adjust all the parameters which affect the vulcanization process, and in particular the vulcanization timetable which is normally adjusted to optimize the vulcanization process.
The method is a tool which is reliable, flexible, and easily used by an engineer (or process engineer) who is skilled in vulcanization processes. The method provides information both on the final state of the vulcanization process and on its variation in time, and details its characteristics within the structure of the tire. This enables the engineer to find critical problems and develop suggestions for their solution.